Finite Group Databasebeta

← #14544215

Subgroups — #14544215

Order 2176.

264 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11763827C211yesmaximal, characteristic, complemented
2#11763753C211yesmaximal, characteristic, complemented
3#11763661C214yesmaximal, complemented
4#11763360C211yesmaximal, characteristic
5C2×#63256—21no—
6C2×C4⋊#595—21no—
7C17×C4⋊Q8C411yescharacteristic, complemented
8#10587633—21no—
9#10587581—21no—
10#10587581C2212yes—
11#10587579—21no—
12#10587579C412yescomplemented
13#10587560C411yescharacteristic, complemented
14C42×D17C2211yescharacteristic
15(C2×#595)⋊C4—21no—
16(C2×#595)⋊C4C2212yes—
17#10587544—21no—
18#10587543C2212yes—
19C4×#3624—21no—
20C22×#595—22no—
21C2×Q8×C17—21no—
22#63256—42no—
23#63256—42no—
24C2×D68—22no—
25C2×D68—21no—
26C2×D68—21no—
27C2×D68C2×C412yes—
28C2×C4×D17—22no—
29C2×C4×D17D411yescharacteristic
30C2×C4×D17D411yescharacteristic
31C2×C4×D17C2311yescharacteristic
32C2×#3624—22no—
33C4⋊#595—42no—
34C4⋊C4×C17—21no—
35C4⋊C4×C17C2×C412yes—
36C42×C17C2×C411yescharacteristic
37#63227—22no—
38#63227—22no—
39C4×Dic17C2×C411yescharacteristic
40C4×Dic17D411yescharacteristic
41C4×Dic17D411yescharacteristic
42C22×D17—22no—
43C22×D17C2×D411yescharacteristic
44C2×#595—42no—
45C2×#595—42no—
46C2×#595—42no—
47Q8×C17—42no—
48C2×C4×C17—22no—
49C2×C4×C17C22⋊C411yescharacteristic
50C2×C4×C17C22⋊C411yescharacteristic
51C2×C4×C17C22×C411yescharacteristic
52C2×Dic17C22⋊C411yescharacteristic
53C2×Dic17C22⋊C411yescharacteristic
54C2×Dic17C2×D411yescharacteristic
55D68—42no—
56D68—42no—
57D68—42no—
58D68—42no—
59D68—42no—
60C4×D17—41no—
61C4×D17—41no—
62C4×D17—44no—
63C4×D17D812yes—
64C4×D17SD1612yes—
65#3624—42no—
66#1517—171nomaximal, Sylow
67C22×C17C2×C22⋊C411yescharacteristic
68C2×D17—21no—
69C2×D17—21no—
70C2×D17—42no—
71C2×D17—42no—
72C2×D17—42no—
73C2×D17C2×D811yescharacteristic
74C2×D17C2×SD1611yescharacteristic
75#595—82no—
76C4×C17—21no—
77C4×C17—21no—
78C4×C17—42no—
79C4×C17#10212yes—
80Dic17—21no—
81Dic17—21no—
82Dic17#10212yes—
83#532—171no—
84#431—171no—
85#382—171no—
86#327—174no—
87C2×C17#41011yescharacteristic
88C2×C17C2×#10211yescharacteristic
89C2×C17#42111yescharacteristic
90D17—21no—
91D17—21no—
92D17—82no—
93C2×#41—341no—
94C4⋊Q8#59511yescharacteristic, complemented
95#127—171no—
96#124—341no—
97#121—172no—
98#121—341no—
99C4×D4—172no—
100C4×D4—341no—
101C2×C4⋊C4—341no—
102C2×C42—171no—
103C4⋊C8—341no—
104C22⋊C8—172no—
105C4×C8—341no—
106#95—172no—
107#95—341no—
108C17#151711yescharacteristic, complemented, Sylow
109#41—682no—
110#41—682no—
111C2×Q8—21no—
112C2×D4—172no—
113C2×D4—342no—
114C2×D4—341no—
115C2×D4—341no—
116C22×C4—171no—
117C22×C4—171no—
118C22×C4—171no—
119C22×C4—342no—
120C22×C4—342no—
121C2×C8—342no—
122C4⋊C4—21no—
123C4⋊C4—682no—
124C4⋊C4C2×#59512yes—
125C22⋊C4—342no—
126C22⋊C4—342no—
127C42—171no—
128C42—171no—
129C42—171no—
130C42C2×#59511yescharacteristic
131C23—171no—
132C23—342no—
133Q8—42no—
134D4—682no—
135D4—682no—
136D4—682no—
137D4—682no—
138D4—682no—
139C2×C4—22no—
140C2×C4—171no—
141C2×C4—172no—
142C2×C4—172no—
143C2×C4—171no—
144C2×C4—171no—
145C2×C4—681no—
146C2×C4—681no—
147C2×C4—684no—
148C2×C4—682no—
149C2×C4—682no—
150C2×C4—682no—
151C2×C4C22⋊#59511yescharacteristic
152C2×C4C22⋊#59511yescharacteristic
153C2×C4C22×#59511yescharacteristic
154C8—682no—
155C22—171no—
156C22—171no—
157C22—341no—
158C22—341no—
159C22—682no—
160C22—682no—
161C22—682no—
162C22C2×C22⋊#59511yescharacteristic
163C4—21no—
164C4—21no—
165C4—42no—
166C4—172no—
167C4—341no—
168C4—341no—
169C4—1362no—
170C4#1058754712yes—
171C2—341no—
172C2—341no—
173C2—1362no—
174C2#1176379011yescharacteristic
175C2C2×#1058754711yescharacteristic
176C2#1176380811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#595
commutatorC2×C4×C17C22×C4
FrattiniC2×C4C22×#595
FittingC17×C4⋊Q8C4
socleC22×C17C2×C22⋊C4
prime radical#11763360C2
cosocleC2×C4×D17C23
hypercenterC4⋊Q8#595
hypocenterC17#1517
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #11763827C2semidirect
2. #11763753C2semidirect
3. #11763661C2semidirect
7. C17×C4⋊Q8C4semidirect
12. #10587579C4semidirect
13. #10587560C4semidirect
94. C4⋊Q8#595semidirect
108. C17#1517semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117638272
#117637532
#117636612
#117633602
#151717